The data file stockton5_small contains observations on 1200 houses sold in Stockton, California, during 1996-1998. [Note: the data file stockton5 includes 2610 observations.] Scale the variable SPRICE to units of \(\$ 1000\), by dividing it by 1000 .

a. Estimate the linear model SPRICE \(=\delta_{1}+\delta_{2} A G E+e\). Interpret the estimated coefficients. Predict the selling price of a house that is 30 years old.

b. Using the results in part (a), plot house selling price against \(A G E\) and show the fitted regression line. Based on the plot, does the model fit the data well? Explain.

c. Estimate the log-linear model \(\ln (S P R I C E)=\theta_{1}+\theta_{2} A G E+e\). Interpret the estimated slope coefficient.

d. Using the results in part (c), compute \(\widehat{S P R I C E}=\exp \left(\hat{\theta}_{1}+\hat{\theta}_{2} A G E\right)\), where \(\hat{\theta}_{1}\) and \(\hat{\theta}_{2}\) are the OLS estimates. Plot \(\widehat{S P R I C E}\) against \(A G E\) (connecting the dots) and SPRICE vs. \(A G E\) in the same graph.

e. Predict the selling price of a house that is 30 years old using \(\widehat{S P R I C E}=\exp \left(\hat{\theta}_{1}+\hat{\theta}_{2} A G E\right)\).

f. Based on the plots and visual fit of the estimated regression lines, which of the two models in (a) or (c) would you prefer? Explain. For each model calculate \(\sum_{i=1}^{1200}(S P R I C E-\widehat{S P R I C E})^{2}\). Is this at all useful in making a comparison between the models? If so, how?